§123. Greek and Latin Number Concepts
First, let us make it clear that we are not talking about number symbols in Greek and Latin—for example, the “Roman numerals” I, V, X, L, C, D, and M—interesting though that topic may be. What this chapter will consider are the actual words developed in the Greek and Latin language to identify and describe numbers. There is some advantage in viewing both languages in the same chapter. All Indo-European number words tend to have a cognate relationship, and that in itself may be revealing. Also, by looking at Greek and Latin side by side we may be able to clarify points of confusion in English, so as to determine which of our number words are descended from one or the other of these classical languages.
As you learned in Part I, Table 2.2, the Latin noun for “number” is numerus—and that is the source of our English word number. The regular Latin ADJECTIVE, therefore, is numeralis (“pertaining to number”), though we use its English derivative numeral more often as noun than adjective. It is an easy step from numerus to the DENOMATIVE verbs (§76) numerare and e-numerare (> E numeration, enumerate).
A cardinal number (< cardo, cardinis, “hinge”) may be considered to be in a pivotal position; in a variety of semantic areas, cardinal came to have the general meaning “chief” or “important.” An ordinal number, in contrast, stands in a “row” or “rank” (ordo, ordinis); its etymology makes it easy to remember this adjectival label that is attached to numbers like “first,” “second,” and “third.”
The Greek equivalent of Latin numerus was ἀριθμος (arithmos), a word that has not given us a simple English noun. Our word arithmetic derives from G ἀριθμητικη, which is short for ἡ ἀριθμητικἠ τἑχνη (hē arithmētikē tekhnē, “the numbering art”). In a later chapter, we’ll see that ἀριθμη-τικος is a standard adjective form, derived regularly from the verb ἀριθμειν (base ἀριθμη-), “to number,” “to count.”
We already know that geometry was originally “earth measurement.” Among the other branches of mathematics (< μαθη, “things learned”), algebra is a loan-word from Arabic (< al-jabr), and trigonometry will be explained later in this chapter.